Interest-only loans and sinking funds | Year 12

01 / LEARN

The idea, step by step

Interest-only payments leave the principal owing

An interest-only loan of principal $P$ at periodic rate $i$ charges $P i$ each period if the rate and principal remain constant. These payments cover interest but do not repay $P$ . The principal is still due at the end unless a separate repayment is made.

A sinking fund is a separate savings account intended to build the amount needed at the debt date. Its interest rate may differ from the borrowing rate. Write one equation for loan interest and another for savings.

I = P i, S = R \frac{{(1 + j)}^{n} - 1}{j}

Combine the cash-flow amounts, not the rates

For equal end-of-period deposits, solve $R = S / s_{n} (j)$ . The regular budget needs to cover both the loan interest and the sinking-fund deposit. This sum is an outflow, but part of it is building an asset rather than paying interest.

When comparing with a reducing-balance loan, specify the same principal and end date and account for all cash flows. A high assumed sinking-fund return makes the projected deposit smaller, but the target depends on that assumption being met.

A common trap

Using the borrowing rate in the sinking-fund formula without checking the savings rate.

Instead: The debt and the savings account are separate models with separately stated rates.

02 / WORKED EXAMPLES

See the thinking

Example 1

Build the model

An interest-only loan is AUD 30,000 at 6% annually. Find its annual interest payment and the principal still owing after 5 interest payments.

Each payment is $30000 \times 0.06 = 1800$ .
None of that payment reduces the loan principal.

Annual interest AUD 1,800.00; principal still owing AUD 30,000.00.

Example 2

Use the model to make a decision

A sinking fund must reach AUD 30,000 in 5 years. At 4% annually, find each equal year-end deposit.

Set $30000 = R ({(1.04)}^{5} - 1) / 0.04$ .
Divide by the five-period savings factor.

AUD 5,538.81

Check your understanding

A no-interest sinking fund must reach AUD 18,000 after 36 month-end deposits. Find each deposit.

Show answer

AUD 500.00

At zero interest, $S = n R$ . $R = 18000 / 36 = 500$ .

03 / WORKSHEET

Your turn

6 questions · 17 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the monthly interest-only payment on AUD 48,000 at 6% nominal annually, charged monthly.
3 marks
A no-interest sinking fund must reach AUD 18,000 after 36 month-end deposits. Find each deposit.
3 marks
For a loan with annual interest-only cost AUD 1,200 and a sinking-fund deposit AUD 2,600 each year, find the annual cash outflow.
3 marks
A sinking fund has AUD 4,000 now and must reach AUD 15,000 in 4 years at 3%. Find each year-end deposit.
3 marks
A fund accumulates AUD 24,000 from 6 deposits of AUD 3,500. Find the interest earned by the fund.
3 marks
An interest-only loan and sinking fund share a 5-year end date. Explain why interest-only payments alone do not meet the final debt.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the monthly interest-only payment on AUD 48,000 at 6% nominal annually, charged monthly.
3 marks
Monthly rate is $0.06 / 12 = 0.005$ .
Interest is $48000 \times 0.005 = 240$ .
AUD 240.00
A no-interest sinking fund must reach AUD 18,000 after 36 month-end deposits. Find each deposit.
3 marks
At zero interest, $S = n R$ .
$R = 18000 / 36 = 500$ .
AUD 500.00
For a loan with annual interest-only cost AUD 1,200 and a sinking-fund deposit AUD 2,600 each year, find the annual cash outflow.
3 marks
Both payments must be budgeted.
$1200 + 2600 = 3800$ ; only the AUD 1,200 is loan interest.
AUD 3,800.00
A sinking fund has AUD 4,000 now and must reach AUD 15,000 in 4 years at 3%. Find each year-end deposit.
3 marks
Grow the current savings: $4000 {(1.03)}^{4}$ .
The deposits must supply the remaining target.
Divide that remainder by $s_{4} (0.03)$ .
AUD 2,509.30
A fund accumulates AUD 24,000 from 6 deposits of AUD 3,500. Find the interest earned by the fund.
3 marks
Total deposits is $6 \times 3500 = 21000$ .
Fund interest is $24000 - 21000 = 3000$ .
AUD 3,000.00
An interest-only loan and sinking fund share a 5-year end date. Explain why interest-only payments alone do not meet the final debt.
2 marks
Track the principal separately from periodic interest.
Confirm the fund target matches the debt still owing at maturity.
They pay for borrowing during the term but do not reduce the principal; the sinking fund or another source must provide the final principal.

Checking saved progress…

Continue learning

Reducing-balance loans

Next lesson

Curriculum reference & lesson scope

SACE Board of South Australia

Stage 2 General Mathematics financial models: investments and annuities, superannuation, income streams and borrowing. Original practice uses supplied hypothetical rates, taxes and fees; statutory or commercial conditions are not inferred.

Official curriculum source ↗

Back to Financial mathematics